Internal problem ID [11692]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {2 y^{2} x +\left (2 x^{2} y+6 y^{2}\right ) y^{\prime }=-3 x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 87
dsolve([(3*x^2+2*x*y(x)^2)+(2*x^2*y(x)+6*y(x)^2)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (1134-54 x^{3}-x^{6}+6 \sqrt {3 x^{9}+18 x^{6}-3402 x^{3}+35721}\right )^{\frac {1}{3}}}{6}+\frac {x^{4}}{6 \left (1134-54 x^{3}-x^{6}+6 \sqrt {3 x^{9}+18 x^{6}-3402 x^{3}+35721}\right )^{\frac {1}{3}}}-\frac {x^{2}}{6} \]
✓ Solution by Mathematica
Time used: 4.797 (sec). Leaf size: 103
DSolve[{(3*x^2+2*x*y[x]^2)+(2*x^2*y[x]+6*y[x]^2)*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (-x^2+\sqrt [3]{-x^6-54 x^3+6 \sqrt {3} \sqrt {x^9+6 x^6-1134 x^3+11907}+1134}+\frac {x^4}{\sqrt [3]{-x^6-54 x^3+6 \sqrt {3} \sqrt {x^9+6 x^6-1134 x^3+11907}+1134}}\right ) \]